Top Banner
CEE 160L – Introduction to Environmental Engineering and Science Lecture 5 and 6 Mass Balances
30

CE 24L – Introduction to Environmental Engineering and Scienceusers.rowan.edu/~jahan/env.enggI-fall2004/MAK Mass Balance Lecture... · CEE 160L –Introduction to Environmental

May 29, 2018

Download

Documents

phungquynh
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Page 1: CE 24L – Introduction to Environmental Engineering and Scienceusers.rowan.edu/~jahan/env.enggI-fall2004/MAK Mass Balance Lecture... · CEE 160L –Introduction to Environmental

CEE 160L – Introduction to Environmental Engineering and

Science

Lecture 5 and 6

Mass Balances

Page 2: CE 24L – Introduction to Environmental Engineering and Scienceusers.rowan.edu/~jahan/env.enggI-fall2004/MAK Mass Balance Lecture... · CEE 160L –Introduction to Environmental

Mass Balance (MB)

• Very important tool

– Track pollutants in the environment

– Reactor/treatment design

• Basis: Law of Conservation of Mass

– Mass can neither be created nor destroyed.

Page 3: CE 24L – Introduction to Environmental Engineering and Scienceusers.rowan.edu/~jahan/env.enggI-fall2004/MAK Mass Balance Lecture... · CEE 160L –Introduction to Environmental

Control Volume

• MB performed over specific control volumes

– Well-defined system boundaries

• Control volume (CV)

– Specific region in space for which MB is written

– Define mass flowrates into and out of system.

Page 4: CE 24L – Introduction to Environmental Engineering and Scienceusers.rowan.edu/~jahan/env.enggI-fall2004/MAK Mass Balance Lecture... · CEE 160L –Introduction to Environmental

Control Volume Examples

• Entire Earth

• Watershed

• Airshed

• Lake

• Sand filter

• Sediment Particle

Page 5: CE 24L – Introduction to Environmental Engineering and Scienceusers.rowan.edu/~jahan/env.enggI-fall2004/MAK Mass Balance Lecture... · CEE 160L –Introduction to Environmental

General Control Volume

Control

Volume

Mass

Inputs

Mass

Outputs Mass due to Physical,

Chemical, and/or Biological

Reactions

Page 6: CE 24L – Introduction to Environmental Engineering and Scienceusers.rowan.edu/~jahan/env.enggI-fall2004/MAK Mass Balance Lecture... · CEE 160L –Introduction to Environmental

General Guidelines for Solving Mass Balance Problems

1. Draw system as a diagram.

– Include flows (inputs and outputs) as arrows.

2. Add numerical information to diagram.

– Flow rates, concentration, reaction rates, etc.

3. Draw dotted line around process component(s) to be balanced.

– This is the CV!

Page 7: CE 24L – Introduction to Environmental Engineering and Scienceusers.rowan.edu/~jahan/env.enggI-fall2004/MAK Mass Balance Lecture... · CEE 160L –Introduction to Environmental

General Guidelines for Solving Mass Balance Problems (cont’d)

4. Decide what material is to be balanced.

– Air, water, pollutant

5. Write MB equation.

– Then, substitute numbers into equation.

6. If only one unknown, solve for that variable.

7. If > one unknown, repeat the procedure.

• Use different CV

• Or use different material for same CV

Page 8: CE 24L – Introduction to Environmental Engineering and Scienceusers.rowan.edu/~jahan/env.enggI-fall2004/MAK Mass Balance Lecture... · CEE 160L –Introduction to Environmental

Overall mass balance between times t and t+∆t(mass at time t+∆t) =

(mass at time t) +

(mass entered system between t and t+∆t)-

(mass exited between t and t+∆t) +

(mass generated/consumed by reaction processes between t and t+∆t)

Page 9: CE 24L – Introduction to Environmental Engineering and Scienceusers.rowan.edu/~jahan/env.enggI-fall2004/MAK Mass Balance Lecture... · CEE 160L –Introduction to Environmental

Overall mass accumulation (∆M/∆t) between times t and t+∆t

(mass at time t+∆t) - (mass at time t) =∆t+

(mass entered system between t and t+∆t)∆t-

(mass exited between t and t+∆t)∆t+

mass generated/consumed by reaction processes between t and t+∆t

∆t

Page 10: CE 24L – Introduction to Environmental Engineering and Scienceusers.rowan.edu/~jahan/env.enggI-fall2004/MAK Mass Balance Lecture... · CEE 160L –Introduction to Environmental

In the limit (∆t0) gives the overall rate of mass accumulation rate

(rate mass accumulation) =+

(rate mass influx)-

(rate mass outflux) +

(rate net mass production/consumption)

dM/dt = dMin/dt – dMout/dt +dMrxn/dt

Reactionterm

Page 11: CE 24L – Introduction to Environmental Engineering and Scienceusers.rowan.edu/~jahan/env.enggI-fall2004/MAK Mass Balance Lecture... · CEE 160L –Introduction to Environmental

Continuous stirred tank reactors (CSTR)

Fio is the molar flow rate inlet of species i, Fi the molar flow rate outletV is the tank volumeni is the stoichiometric coefficient. ti is the residence time (the average amount of time a discrete quantity of reagent spends inside the tank)

For reaction Aproducts reaction rate is given

by r=kCA Consumption of reactant A generally follows

http://en.wikipedia.org/wiki/Continuous_stirred-tank_reactor

Rxnterm

Page 12: CE 24L – Introduction to Environmental Engineering and Scienceusers.rowan.edu/~jahan/env.enggI-fall2004/MAK Mass Balance Lecture... · CEE 160L –Introduction to Environmental

Commercial uses of CSTR

• Fermentors for biological processes in many industries

• Brewing

• Antibiotics production

• Cell culture

• Waste treatment

• http://encyclopedia.che.engin.umich.edu/Pages/Reactors/CSTR/CSTR.html

Page 13: CE 24L – Introduction to Environmental Engineering and Scienceusers.rowan.edu/~jahan/env.enggI-fall2004/MAK Mass Balance Lecture... · CEE 160L –Introduction to Environmental

A Simple Control Volume

Continuously Stirred Tank Reactor (CSTR) Model

A Well-Mixed Airshed or Lake

Area, A

OR Lake with MTBE

concentration, CMTBE, in

OR Lake with MTBE

concentration, CMTBE, out

Volume, V

Wind with ozone concentration, Cozone, in

Wind velocity, u

Wind with ozone

concentration, Cozone, out

Page 14: CE 24L – Introduction to Environmental Engineering and Scienceusers.rowan.edu/~jahan/env.enggI-fall2004/MAK Mass Balance Lecture... · CEE 160L –Introduction to Environmental

CSTR Model

• Fluid particles entering the reactor are instantaneously mixed throughout the reactor.– No concentration or thermal gradients exist.

– Creactor = Ceffluent

• Rapid dilution of influent concentration

• Smoothes time-varying input flow and concentrations

Page 15: CE 24L – Introduction to Environmental Engineering and Scienceusers.rowan.edu/~jahan/env.enggI-fall2004/MAK Mass Balance Lecture... · CEE 160L –Introduction to Environmental

Mass Accumulation Term

T

M

dt

dCV

dt

dm Volume,Constant For

T

M

dt

d(VC)

dt

dm onAccumulati

Concentration of

water, air, pollutant

Page 16: CE 24L – Introduction to Environmental Engineering and Scienceusers.rowan.edu/~jahan/env.enggI-fall2004/MAK Mass Balance Lecture... · CEE 160L –Introduction to Environmental

Steady State

• No change in mass in reactor with time

• All flow rates, T, P, concentrations, and liquid levels are constant with time.

• At steady state– Mass can be entering and leaving reactor

– Reactions not necessarily at equilibrium

– However, inputs, outputs and rates of consumption and generation balance each other.

Page 17: CE 24L – Introduction to Environmental Engineering and Scienceusers.rowan.edu/~jahan/env.enggI-fall2004/MAK Mass Balance Lecture... · CEE 160L –Introduction to Environmental

Mass Balance Terms

0dt

dm with timechanges system stateUnsteady

0dt

dm with timechangenot does system stateSteady

Accumulation Term

Rate of mass coming in (Input)

Rate of mass going out (Output)

Area, A

uout, Cout

Volume V

uin, Cin

dmin/dt = Qin x Cin

dmout/dt = Qout x Cout

Qout x CoutQin x Cin

Page 18: CE 24L – Introduction to Environmental Engineering and Scienceusers.rowan.edu/~jahan/env.enggI-fall2004/MAK Mass Balance Lecture... · CEE 160L –Introduction to Environmental

Overall Balance for a Simple Constant Volume CSTR

• Neglecting reactions, additional sources/sinks for now

Accumulation[ ] = Inputs[ ]- Outputs[ ]± Generation/Consumption[ ]

VdC

dt= Qin Cin -QoutCout

where :

V = volume

C = concentration (mass/volume)

Q = volumetric flowrate

Concentration in the

reactor

Page 19: CE 24L – Introduction to Environmental Engineering and Scienceusers.rowan.edu/~jahan/env.enggI-fall2004/MAK Mass Balance Lecture... · CEE 160L –Introduction to Environmental

Consider an overflowing rain barrel

What is the volume?What is Qin?What is Cin?

Is it well stirred?What is Qout?What is Cout?

Page 20: CE 24L – Introduction to Environmental Engineering and Scienceusers.rowan.edu/~jahan/env.enggI-fall2004/MAK Mass Balance Lecture... · CEE 160L –Introduction to Environmental

Example 1: Lake Contaminated with MTBE(Steady State)

Cin,(1) Qin(1), w

Cout, Qout, w

Well-mixed

Cin(2), Qin(2), w

Where: C = concentration of MTBE [mg MTBE/L]

Q = volumetric flowrate of water [L/min]

w = density of water [mg/L]

(Therefore, a CSTR)

C

Page 21: CE 24L – Introduction to Environmental Engineering and Scienceusers.rowan.edu/~jahan/env.enggI-fall2004/MAK Mass Balance Lecture... · CEE 160L –Introduction to Environmental

1. Steady State Mass Balance on Lake Water Only

C

Cin,(1) Qin(1), w

0 mg/L, 5000 L/min

Cout, Qout, w

Cin(2), Qin(2), w

0 mg/L, 1000 L/min

At steady state there if no net accumulation or depletion of water in the lake

Qout=Qin(1)+Qin(2)=6000L/min

Two rivers running in

One river running out

Page 22: CE 24L – Introduction to Environmental Engineering and Scienceusers.rowan.edu/~jahan/env.enggI-fall2004/MAK Mass Balance Lecture... · CEE 160L –Introduction to Environmental

2. Mass Balance on MTBE Lake

C

Cin,(1) Qin(1), w

20 mg/L, 5000 L/min

Cout, Qout, w

6000 L/min Cin(2), Qin(2), w

0 mg/L, 1000 L/min

At steady state then amount of water and MTBE that flows in has to equal the amount of water MTBE and water that flows out

To balance the mass then

CoutQout=[Cin(1)+Cin(2)]x[Qin(1)+Qin(2)]=20mg/L*6000L/min

Cout6000L/m=(20mg/L)(5000L/min+1000L/min)

Cout=20*5000/6000=16.7mg/L (inflow of clean 2nd river dilutes MTBE outflow)

Page 23: CE 24L – Introduction to Environmental Engineering and Scienceusers.rowan.edu/~jahan/env.enggI-fall2004/MAK Mass Balance Lecture... · CEE 160L –Introduction to Environmental

Example 2: Lake Contaminated with MTBE (Steady State)

Where: C = concentration of MTBE [mg MTBE/L]

Q = volumetric flowrate of water [L/min]

w = density of water [mg/L]

What happens if Qin(2) = 0?

At steady state, will C in lake

will

Increase?

Decrease?

Remain the same? Cin,(1) Qin(1), w

Cout, Qout, w

Well-mixed

Cin(2), Qin(2), w

Page 24: CE 24L – Introduction to Environmental Engineering and Scienceusers.rowan.edu/~jahan/env.enggI-fall2004/MAK Mass Balance Lecture... · CEE 160L –Introduction to Environmental

Example 2: Lake Contaminated with MTBE (Steady State)

If 20mg/L of MTBE and 5000L/min water flows in,

then at steady state 20mg/L of MTBE and 5000L/min

water must flow out.

What happens if Qin(2) = 0?

At steady state, will C in lake

will

Increase?

Decrease?

Remain the same? Cin,(1) Qin(1), w

Cout, Qout, w

Well-mixed

Cin(2), Qin(2), w

Page 25: CE 24L – Introduction to Environmental Engineering and Scienceusers.rowan.edu/~jahan/env.enggI-fall2004/MAK Mass Balance Lecture... · CEE 160L –Introduction to Environmental

Residence Time

• Residence time=amount present/rate of removal

1. Hydraulic residence time (HRT)

Reactor in Stays Fluid Time Average

System ofOut RateFlow

System in Volume

Q

V θ HRT

out

h

Example: HRT in drinking water distribution system = 1.3 d

Page 26: CE 24L – Introduction to Environmental Engineering and Scienceusers.rowan.edu/~jahan/env.enggI-fall2004/MAK Mass Balance Lecture... · CEE 160L –Introduction to Environmental

Residence Time

• Residence time=amount present/rate of removal

2. Pollutant residence time (PRT)

PRT = CinVin

CoutVout

= Pollutant Mass in System

Pollutant Mass Out of System

= Average Time Pollutant Mass Stays in Reactor

Page 27: CE 24L – Introduction to Environmental Engineering and Scienceusers.rowan.edu/~jahan/env.enggI-fall2004/MAK Mass Balance Lecture... · CEE 160L –Introduction to Environmental

In the limit (∆t0) gives the overall rate of mass accumulation rate

(rate mass accumulation) =+

(rate mass influx)-

(rate mass outflux) +

(rate net mass production/consumption)

dM/dt = dMin/dt – dMout/dt +dMrxn/dt

Reactionterm

Page 28: CE 24L – Introduction to Environmental Engineering and Scienceusers.rowan.edu/~jahan/env.enggI-fall2004/MAK Mass Balance Lecture... · CEE 160L –Introduction to Environmental

Mass balance of fish farm

Mass influx?

Mass outflux?

Reaction terms?

Page 29: CE 24L – Introduction to Environmental Engineering and Scienceusers.rowan.edu/~jahan/env.enggI-fall2004/MAK Mass Balance Lecture... · CEE 160L –Introduction to Environmental

Mass balance of fish farm

Mass influx : mass fish added initially, fish feed added, inspired O2

Mass outflux: uneaten feed, fish death, fish waste, respired CO2

Reaction terms: mass increase of fish

Page 30: CE 24L – Introduction to Environmental Engineering and Scienceusers.rowan.edu/~jahan/env.enggI-fall2004/MAK Mass Balance Lecture... · CEE 160L –Introduction to Environmental

Consider other factors

http://www.waikatoregion.govt.nz/Environment/Natural-resources/coast/Coastal-pressures/Marine-farming/Marine-farming-science-projects/

Mass accumulation?

Mass consumption?

In flows?

Out flows?